Multi-channel signal processing systems often contain a larger number of sensors than there are bands of information to be extracted. Namely, they may be characterized as containing n sensors for deriving m bands of information, where n&gt;m. For example, a color imagery sensing system, such as employed for high definition television, may, on occasion, contain four image sensors, three of which provide relatively low spatial resolution measurements of the red, green and blue components of an image, such as the red (R), green (G) and blue (B) density of a color film, while the fourth sensor provides a relatively high spatial resolution, luminance-representative (L) output signal. A low spatial frequency luminance signal is generated by resampling the original high resolution luminance signal, so as to replicate the resolution at which the red, green and blue signals are measured. Subtracting this low frequency luminance from the original luminance signal yields only its high frequency component. (Aside from this subtraction step, the low frequency luminance information is not used.) The resulting high frequency component is then added to the red, green and blue signals to produce high frequency information for these channels.
Due to the imperfect nature of the sensors, each output signal inherently possesses some degree of sensor-induced noise, so that the output may be expressed as the sum of an intended parameter p.sub.i, plus a noise component n.sub.pi associated with the sensor's measurement of that parameter. Consequently, reducing the magnitude of this noise component would enable the system to provide a more faithful reconstruction of its input image. Fortunately, since a typical film strip contains only three dyes, the system is essentially measuring the values of three parameters (dye densities) on the basis of four measurements (red, green blue and luminance transmittances). Moreover, even when the system is making measurements on a scene which contains a full spectrum of colors (e.g. the real world), because the spectral sensitivity of the luminance sensor usually overlaps that of the other sensors (e.g. RGB color sensors), the (low frequency) luminance component will contain information that is related to the parameter measurements in the color sensor outputs.